多物理多准则形状optimization的解析研究
An analytical study in multi physics and multi criteria shape optimization
摘要：
一个简单的多物理系统的潜在流动的流体通过一个机械部件，如涡轮叶片，放置在护罩，数学建模。然后，我们考虑一个多准则形状最优化问题，当组件的形状是允许变化的一组特定的二阶Hölder连续可微变换的基线形状与边界的相同的连续类。作为目标函数，我们考虑一个简单的损失模型的流体动力学效率和组件的故障概率，由于重复应用的负载，干从流体的静压。对于这个多物理系统，它表明，在一定条件下的Pareto前沿是最大的意义上的Pareto前沿的可行集重合的Pareto前沿的闭包。我们还表明，所有的最佳形式的集合相对于标量化技术变形连续（在Hausdorff度量）的偏好参数。
英文摘要：
A simple multi-physical system for the potential flow of a fluid through a shroud in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi criteria shape optimization problem, when the shape of the component is allowed to vary under a certain set of 2nd order Hölder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid's static pressure. For this multi-physical system, it is shown that under certain conditions the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.
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